4 Answers
4

First off, measuring the temperature of an empty pan will only tell you so much. That temperature is a result of the balance of your stove putting heat into the pan and the pan transferring that heat to the surrounding air, which means it depends on the pan, and as soon as you put anything in the pan the temperature is going to change. (See also What temperatures do low-medium-high on the stove correspond to?.)

So, 260F is certainly hot enough to scramble eggs. They'll be fully cooked by around 160F, though at that point they might be a bit softer than you're used to. But the fact that the pan only reaches 260F really suggests that the stove isn't putting much heat into the pan, so once you add eggs to the pan, it might take an awfully long time for them to get hot enough to cook.

And a stove that can only heat an empty pan to 260F sounds like incredibly low power. Most stoves can easily get empty pans up to at least 400-500F. You might want to see if you can get the stove repaired or replaced.

I made some measurements with an IR probe:
At 135 to 140 Celsius (275-285 Fahrenheit) I get a decent result. However, it seems it would be even better with a slightly lower temperature. So 130 Centigrade or 265-270 Fahrenheit ought to give a good result.